Reports

(2(11)/2017) Dorota Leszczyńska-Jasion, On certain generalizations of the concepts of erotetic implication and erotetic search scenario. Research Report

Abstract: In this research report I analyse a generalization of the concept of erotetic search scenario (ESS), and show how each such general scenario may be transformed into ESS in the original sense. I also propose a new, proof-theoretic account of the notion of ESS.

Abstract: In this short note we show how some one-sided erotetic calculi for Classical Propositional Logic (hereafter: CPL) enable a relatively easy conversion of a CPL-formula into equivalent CPL-formulas in Disjunctive Normal Form (DNF) and in Conjunctive Normal form (CNF). A practical advantage of the proposed approach is the absence of steps which often lead to mistakes when “standard” conversion procedures are performed by humans, namely applying distributivity rules.

Abstract: Some non-monotonic relations of single- and multiple-conclusion entailment based on minimally inconsistent sets are defined and analyzed. A proof-theoretic account of minimally inconsistent sets is provided. Applications concerning minimal disjunctions, contraction, and argument analysis are presented.

Introduction: This research report presents some results on question raising as modelled in the logic of permittance (Wisniewski [2013]). The rst section of the report oers some theorems concerning basic semantic notions of this logic: permittance, transmission of permittance, logical entailment, and epistemic modality (of knowledge in a state”). In the second section some paradoxes of irrelevant permittance evocation of questions are given. The third section presents examples of two versions of permittance erotetic implication, and some theorems on their relationships. The report is not self-contained: for all the notions and symbols used here the reader should refer to Wisniewski [2013].

Abstract: We report a research on correlations between level of fluid intelligence and fluencies in two kinds of deductions, simple (syllogistic reasoning) and dificult ones (erotetic reasoning), and on the impact of learning logic on fluencies in deductive reasoning. We observed that although participants of higher ability (with respect to fluid intelligence) performed better than participants of lower ability in both kinds of deductive tasks, those who undergone extensive training in formal logic obtained significantly higher results than the rest of this group in tasks involving dificult deductions. We conclude on this basis that fluency in dificult deductions, while related to fluid intelligence, is related also to subjects’ educational experience and that this does not hold in case of simple deductions.

Abstract: In this paper I shall give a method of identifying minimal truth conditions and minimal synthetic tableaux for a given formula A of Classical Propositional Calculus, via reduction of clausal Disjunctive Normal Form of A.

Abstract: Inferential Erotetic Logic (IEL) and Inquisitive Semantics (INQ) give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: (1) a disjunction of all the direct answers to an evoked question is always inquisitive; (2) a formula is inquisitive if, and only if it evokes a yes-no question whose affirmative answer expresses a possibility for the formula; (3) inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and (4) each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question.

Abstract: Our aim is to show that two different accounts of erotetic search scenarios — namely, e-scenarios defined as families of interconnected sequences and e-scenarios defined as labelled trees — may be considered as equal.